Abstract

The authors consider a minimal cross-catalytic self-replicating system of only two cross-catalytic templates that mimics the R3C ligase ribozyme system of Dong-Eu and Joyce [Chem. Biol.11, 1505 (2004)]. This system displays considerably more complex dynamics than its self-replicating counterpart. In particular, the authors discuss the Poincaré-Andronov-Hopf bifurcation, canard transitions, excitability, and hysteresis that yield birhythmicity between simple and complex oscillations.

Received 02 January 2007Accepted 20 February 2007Published online 27 March 2007

Acknowledgments:

The authors would like to thank the National Science Foundation for their financial support through Grant Nos. CHE-0136142 and CHE-0548622 and E. M. Peacock-Villada and D. Morandi for helpful comments.